Time-Consistent Mean-Variance Portfolio Optimization: A Numerical Impulse Control Approach

36 Pages Posted: 27 Nov 2017 Last revised: 29 Aug 2018

See all articles by Pieter Van Staden

Pieter Van Staden

University of Queensland - School of Mathematics and Physics

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Peter Forsyth

University of Waterloo - David R. Cheriton School of Computer Science

Date Written: November 22, 2017

Abstract

We investigate the time-consistent mean-variance (MV) portfolio optimization problem under a realistic context that involves the simultaneous application of different types of investment constraints and modelling assumptions, for which a closed-form solution is not known to exist. We develop an efficient numerical partial differential equation method for determining the optimal control for this problem. Central to our method is a combination of (i) an impulse control formulation of the MV investment problem, and (ii) a discretized version of the dynamic programming principle enforcing a time-consistency constraint. We impose realistic investment constraints, such as no trading if insolvent, leverage restrictions and different interest rates for borrowing/lending. Our method requires solution of linear partial integro-differential equations between intervention times, which is numerically simple and computationally effective. The proposed method can handle both continuous and discrete rebalancings.We study the substantial effect and economic implications of realistic investment constraints and modelling assumptions on the MV efficient frontier and the resulting investment strategies. This includes (i) a comprehensive comparison study of the pre-commitment and time-consistent optimal strategies, and (ii) an investigation on the significant impact of a wealth-dependent risk aversion parameter on the optimal controls.

Keywords: Asset Allocation, Constrained Optimal Control, Time-Consistent, Pre-Commitment, Impulse Control

JEL Classification: G11, C61

Suggested Citation

Van Staden, Pieter and Dang, Duy-Minh and Forsyth, Peter, Time-Consistent Mean-Variance Portfolio Optimization: A Numerical Impulse Control Approach (November 22, 2017). Available at SSRN: https://ssrn.com/abstract=3075819 or http://dx.doi.org/10.2139/ssrn.3075819

Pieter Van Staden

University of Queensland - School of Mathematics and Physics ( email )

Brisbane
St Lucia, QLD 4072
Australia

Duy-Minh Dang (Contact Author)

University of Queensland - School of Mathematics and Physics ( email )

Priestly Building
St Lucia
Brisbane, Queesland 4067
Australia

HOME PAGE: http://people.smp.uq.edu.au/Duy-MinhDang/

Peter Forsyth

University of Waterloo - David R. Cheriton School of Computer Science ( email )

200 University Avenue West
Waterloo, ON
Canada

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